A universal numerical discretization method on different meshes

A universal discretization method is prestented in this paper, it can be used on arbitary meshes.Considering the common properties of all different kinds of meshes, we established this numericaldifference scheme by Taylor series expansion and the least square method.We can obtain the local difference matrix(LDM) and global difference matrix(GDM) on any mesh by this method,then the difference operator can be interpreted as its matrix form in discreted space directly. This skill can apply tomany numerical schemes developed on structured grid, then those schemes will work on arbitary meshes,the complexity of the computation domain will no longer be any problems.In order to verify the skill in this paper, we first compute the numerical difference of an analytical function,and compare the results with the exact solutions. It shows that the method has the 2nd order accuracy as the center difference scheme.Another two examples are numerical simulation of incompressible flow in a two dimension backward-facing step and three dimension driven cavity. The vorticity-stream function equation and Navier-Stokesequations in velocity-pressure form are used respectively. The results in this paper are agreement withthe classical ones on structured meshes. But the method here can be applied on any grid.